Magnetic resonance imaging (MRI) is a non-invasive diagnostic imaging procedure that uses nuclear magnetization and radio waves to produce internal images of a patient. The operation of an MRI scanner is well known but, briefly, an MRI scanner contains magnetic coils that create a strong static magnetic field in which the patient is positioned. Certain atoms in a patient's body that were previously randomly-ordered become aligned along the magnetic field. The scanner then sends a series of bursts or pulses of radio frequency (RF) energy through the patient's body part under examination that excite the “ordered” atoms to specific oscillations around the magnetic field. The atoms give up the RF energy, i.e., generate an RF signal, during the pulsed oscillations and as the atoms return to their respective alignments. The scanner detects the RF signals by appropriate reception or pick-up coils and uses gradient coils to generate non-homogeneous magnetic fields to enable the signals to be spatially coded in all three spatial directions. The scanner processes the coded signals or data to transform them into a visual representation of the scanned patient's body part. In particular, the scanner samples and digitizes the signals, creates a so-called k-space data matrix filled with the digitized complex values of each signal, and generates for display and/or other usage a corresponding MR image from the k -space data matrix by means of a complex Fourier transformation. The MRI scanner acquires three-dimensional image data of the patient's body part for respective “slices” of an area of the body part. The scanner repeats a pre-defined MR image pulse sequence, i.e., the above-described steps for collecting the signals/data, a number of times to collect sufficient data from the excitations to reconstruct the specific image. Ideally, there are little or no variations in the nuclear magnetization during the excitations. However, movement by the patient, voluntary or involuntary, is one of several conditions that may affect the nuclear magnetization and the subsequent MR image reconstruction.
MRI is an important imaging technique due to its flexibility and safety. However, there is a fundamental trade-off in MRI between acquisition time and image quality of the reconstructed images. In many circumstances, it is desirable to decrease the acquisition time so as to reduce the image artifacts resulting from the motion of the patient and from breathing or heart beating; to enable dynamic imaging; and to reduce overall examination times. Many techniques and technologies have been developed to improve image acquisition time.
Parallel imaging is a relatively new technique/technology that is designed to reduce the image acquisition time and has enabled many powerful improvements in routine clinical MRI; in particular, it enables dramatic acceleration of the MRI examination. Generally, an MRI scanner employing parallel imaging accomplishes this by obtaining spatial information from arrays of multiple independent radiofrequency (RF) coil detectors sampling data in parallel rather than from some portion of the spatial encoding which is performed using the gradient coils (typically the phase-encoding gradient). Only a fraction of the phase-encoding lines of image data is then acquired (i.e., under sampling k-space data) since phase encoding consumes much more time compared to the other location encodings. The MRI scanner applies a specialized reconstruction method to the acquired data to reconstruct the missing information, resulting in the full field-of-view (FOV) image in a fraction of the time. Many of the time-consuming image encoding steps can be skipped during the acquisition and then subsequently recovered in post-processing by exploiting the independent observations collected from each RF reception coil. This technique results in a significant decrease in the acquisition time, allowing for shorter examinations or for higher temporal sampling rates in dynamic imaging.
There are several parallel imaging reconstruction methods. One of the leading approaches for image reconstruction in parallel MRI is the GRAPPA method (this is more fully described in an article by M. A. Griswold, P. M. Jakob, R. M. Heidemann, N. Nittka, V. Jellus, J. M. Wang, B. Kiefer, and A. Haase, “Generalized autocalibrating partially parallel acquisitions (GRAPPA)”, Magnetic Resonance in Medicine, 47:1202-1210, 2002). GRAPPA enables image reconstruction for accelerated acquisitions by estimating skipped k-space data through weighted combinations of raw k-space measurements across all channels in the RF receive coil array. Thereafter, the k-space data undergoes Fourier transformation. In contrast, compressed sensing (CS) image reconstruction techniques typically enable image reconstruction of accelerated acquisitions by examining and exploiting sparsity measures phrased in image space. Compressed sensing (CS) reconstructs images from each RF reception coil element with reduced FOV and then merges the images using knowledge of individual coil sensitivities.
Known systems attempt to mitigate the time-consuming nature of magnetic resonance imaging (MRI) processing. In Cartesian Fourier transform-based imaging, k-space is sampled at uniformly spaced intervals along the readout and phase-encode directions. Known systems use accelerated parallel imaging, where multiple receiver coils allow undersampled k-space acquisitions to produce images without aliasing. In addition, compressed sensing (CS) is applied in MRI to reduce the number of samples required to recover approximately sparse images. Given multiple receiver coils, several post-processing techniques, including SENSE (SENSitivity Encoding), SMASH (SMASH (SiMultaneous Acquisition of Spatial Harmonics), GRAPPA (Gene-Ralized Autocalibrating Partially Parallel Acquisition), and SPIR-iT, (Iterative Self-Contained Parallel Imaging reconstruction) synthesize un-aliased images from multi-coil undersampled data, in either k-space or the image domain. GRAPPA and SPIR-iT acquire several additional k-space lines, called autocalibration signal (ACS) lines, to form kernels for use in reconstruction. GRAPPA however assumes uniform undersampling. GRAPPA can be extended to non-uniform Cartesian subsampling at greater computational cost by using multiple kernels, one for each source/target pattern encountered. In contrast, SPIR-iT is another known accelerated parallel imaging system that accommodates non-uniform sampling patterns, since SPIR-iT uses the kernel to enforce consistency between a point in k-space and its neighborhood of k-space points, both acquired and unknown. The known systems reconstruct diagnostically useful images from undersampled data, however, at higher acceleration factors, GRAPPA especially tends to fail due to noise enhancement and unresolved aliasing. Also, SPIR-iT is more computationally intensive than GRAPPA for uniform undersampling.
Compressed sensing (CS) is a framework for reconstructing a sparse signal from fewer samples than is required according to classical sampling theory. A typical CS optimization problem involves minimizing the number of nonzero coefficients of a signal, while remaining consistent with observations. Direct interpretation yields a combinatorially hard problem, but greedy methods yield approximate solutions. One known system operates in the nullspace of an observation matrix (i.e. optimizes over the missing k-space values), preserving the data without the complexity of solving a constrained optimization problem. Known systems also apply CS to single-channel accelerated MRI reconstruction. Parallel imaging and compressed sensing are known methods for reconstructing images from accelerated MR image acquisitions. However, the combination of these two frameworks remains not fully explored.
CS-GRAPPA, CS-SENSE, and L1 SPIR-iT combine parallel imaging methods (GRAPPA, SENSE, and SPIR-iT) with compressed sensing, however these combinations have substantial limitations. CS-GRAPPA combines CS and GRAPPA, alternatingly applying GRAPPA and CS reconstructions to fill missing k-space lines. The iterative structure of this method limits the synergy between sparsity (from CS) and multiple coils (from GRAPPA). CS-SENSE sequentially applies CS to each aliased coil image and combines the CS results using SENSE. Like SENSE, CS-SENSE is highly sensitive to the quality of the estimates of the coil sensitivity profiles. L1 SPIR-iT jointly optimizes both for sparsity and for fidelity to a parallel imaging solution. However, L1 SPIR-iT is computationally complex because the SPIR-IT kernel, unlike the GRAPPA kernel it replaces, needs to be applied repeatedly throughout the process, updating the k-space data for consistency instead of filling in the missing k-space data directly. It would be advantageous to jointly optimize both CS and GRAPPA error measures to produce reconstructed images that are consistent in both k-space and image space. A system according to invention principles combines GRAPPA with CS to improve quality and speed of accelerated MRI image reconstruction.